32 citations · 73 across the 12 of their papers we have counts for
4 papers · 1 filter
A well-posedness theory in Sobolev spaces for the stochastic magnetohydrodynamic equations in the whole space
Ildoo Kim, Minsuk Yang
We prove the existence of a mild solution to the three dimensional incompressible stochastic magnetohydrodynamic equations in the whole space with the initial data which belong to…
An -Lipschitz theory for parabolic equations with time measurable pseudo-differential operators
Ildoo Kim
In this article we prove the existence and uniqueness of a (weak) solution in to the Cauchy problem \begin{align} \notag &\frac{\partial u}{\p…
An -theory for the time fractional evolution equations with variable coefficients
Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim
We introduce an -theory for the quasi-linear fractional equations of the type $$ \partial^α_t u(t,x)=a^{ij}(t,x)u_{x^i x^j}(t,x)+f(t,x,u), \quad t>0, \,x\in \mathbf{R}^d.…
An -theory for parabolic pseudo-differential equations: Calderón-Zygmund approach
Ildoo Kim, Kyeong-Hun Kim, Sungbin Lim
In this paper we present a Calderón-Zygmund approach for a large class of parabolic equations with pseudo-differential operators of arbitrary order $γ\in(0,\infty)…